Mathematical models to help understand developmental biology and cancer

As the understanding of cellular regulatory networks grows, system
dynamics and behaviors resulting from feedback effects of such systems
have proven to be sufficiently complex so as to prevent intuitive
understanding. Mathematical modeling in engineering and in physics
or chemistry has traditionally sought to extrapolate from existing
information and underlying principles to create complex descriptions
of various systems, which could be analyzed or simulated, and from
which further abstractions could be made. However, in studying biological
systems, often only incomplete abstracted hypotheses exist to
explain observed complex patterning and functions.
The challenge has become to show that enough of a network is
understood to explain the behavior of the system. Mathematical
modeling must simultaneously characterize the complex and nonintuitive
behavior of a network, while revealing deficiencies in the
model and suggesting new experimental directions. In this talk, we
describe the process of modeling two biological networks: planar cell
polarity in development, and treated regulatory networks in breast
cancer. We demonstrate the use of the mathematical models, both
in understanding the system behavior, and in suggesting new treatments.